| Titre : | Stochastic Maximum Principle for Optimal Control Problems In Progressive Structure |
| Auteurs : | Ouidad Chabouha, Auteur ; Farid Chighoub, Directeur de thèse |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (50 p.) / couv. ill. en coul / 30cm |
| Langues: | Français |
| Résumé : |
This master's dissertation introduces a straightforward method for dealing with jumps in stochastic processes. Here's an explanation of the key points: The approach we present is simple and easy to apply, which makes it accessible for those working with Stochastic processes can experience sudden changes or "jumps." This method specifically addresses these jumps, making it easier to estimate values within systems that include such dis- continuities, and simplifies the process of making estimates within these systems. This is particularly important as the values we are dealing with become larger, where traditional methods might become more complex or less accurate. This broad applicability ensures that it can be used in various situations without significant limitations. |
| Sommaire : |
Remerciements ii Introduction 1 1 Introduction to Stochastic Computation 4 1.1 Stochastic Processes . . . . . . . . . . . . 4 1.1.1 Brownian Motion . . . . . . . . . . . . . . . . . . . 6 1.2 Martingales . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Stochastic Integration and ItÙís Formula . . . . . . . . . . . . . . 7 1.3.1 Wiener Integral . . . . . . . . . . . . . . . . . . 8 1.3.2 The ItÙís integral . . . . . . . . . . . . . . . . . .. . . 9 1.4 ItÙís Formula . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Existence and Uniqueness of Solutions for a Stochastic Di§erential Equation with Jumps 12 2.1 Stochastic Integral of Random Measure . . . . . . . . . 13 2.2 Existence and Uniqueness . . . . . . . . . . . . . . . . .. . 22 3 The Maximum Principle for Progressive Optimal Stochastic Control Problems with Random Jumps 34 3.1 Statement of the Problem . . . . . . . . . . . . . . . . . . 34 3.2 Spike Variation . . . . . . . . . . . . . . . . . . . . . . 37 3.3 Adjoint Equations and the Maximum Principle. . . . . . 42 Conclusion 46 Bibliographie 46 Abbreviations and Notations 49 Conclusion 50 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1317 | Mémoire master | bibliothèque sciences exactes | Consultable |
